Talking Angela is a mobile game (formerly a chatbot), developed by Slovenian studio Outfit7 as part of the Talking Tom & Friends series. It was released on 13 November 2012 and December 2012 for iPhone, iPod and iPad, January 2013 for Android, and January 2014 for Google Play. The game's successor, the My Talking Angela game, was released in December 2014. The game takes place in a café in Paris and allows players to interact with Angela, an anthropomorphic white cat in different ways. Players can use coins to purchase makeup, accessories and items, as well as drinks that will trigger different visual effects. The fortune cookie button causes Angela to read out a fortune cookie, while the bird icon will prompt birds to fly around the screen, or have Angela feed them. Players can also pet or poke Angela, as well the café's sign. Prior to their removal, the game featured a chat system and a camera button. Users can engage in conversations with Angela, ask for quizzes or initiate a short snippet of the song "That's Falling In Love". If the player was to type in "Who is an idiot?", Angela would respond with a random swear word. Additionally, inquiring Angela about sexual topics would cause her to reply with "Do you want to talk about sex?", though she will quickly change the topic regardless of what the player writes next. A hoax claiming that Angela's eyes were hidden cameras that enabled hackers or paedophiles to watch children was spread. Despite the claims, Snopes and The Guardian found no evidence. Due to the hoax, Angela received a blue dress, as well as an altered eye asset with a different reflection, and later the chat and camera functions were removed altogether. == Hoaxes == In February 2014, Talking Angela was the subject of an Internet hoax alleging that the application was a front for child predators to exploit children. The rumor, which was widely circulated on Facebook and various websites claiming to be dedicated to parenting, claims that a sinister sexual predator or hacker, asked children for private personal information using the game's text-chat feature. Other versions of the rumour even attributed the disappearance of a child to the game; one news report claimed that a seven year old boy disappeared after downloading the app. Another variation included that it was run by a paedophile ring, citing a man that could be seen in Angela's eyes. The app's developers, Outfit7, later gave a statement refuting the hoaxes. The hoax was eventually debunked by Snopes, a fact-checking website. The site's owners, Barbara and David Mikkelson, reported that they had tried to "prompt" it to give responses asking for private information, but were unsuccessful, even when asking it explicitly sexual questions. While it is true that, in the game with child mode off, Angela does ask for the user's name, age and personal preferences to determine conversation topics, Outfit7 has said that this information is all "anonymized" and all personal information is removed from it. It is also impossible for a person to take control of what Angela says in the game, since the game is based on chatbot software. When the mode was turned on, the chat feature was disabled, meaning no personal questions could be asked. In 2015, the hoax was revived on Facebook, which prompted online security company Sophos and The Guardian to debunk it again. Sophos employee Paul Ducklin wrote that the message being posted on Facebook promoting the hoax was "close to 600 rambling, repetitious words, despite claiming at the start that it didn't have words to describe the situation. It's ill-written, and borders on being illiterate and incomprehensible." Bruce Wilcox, one of the game's programmers, attributed the hoax's popularity to the fact that the chatbot program in Talking Angela aimed to sound realistic. Concern was raised that the game's child mode may have been too easy for children to turn off. It allowed them to purchase "coins", premium currency in the game, via iTunes, and enabled the chat feature. While not "connecting your children to paedophiles", this still raised concerns according to The Guardian. === Impact === The scare significantly boosted the game's popularity, and was credited with helping the app enter the top 10 free iPhone apps soon after the hoax became widely known in February 2015,In the truth the reason there is a man in Angela’s eyes is because of pareidoila, the ability to see through diamonds and other minerals and water bodies and shiny objects,which is the reason why players notice a man in her eyes,The truth is that being Angela’s eyes simply serve as a reflective surface,Because of the low quality of this reflection the reflection was mistaken for a humanoid figure. oref>Smith, Josh (19 February 2014). "Talking Angela App Scare Skyrockets App to Top of Charts". GottaBeMobile.com. Archived from the original on 2 April 2016. Retrieved 10 May 2014. and third most popular for all iPhone apps at the start of the following month. In 2016, Outfit7 removed the chat feature along with the camera function from the app due to this controversy, though this decision was met with criticism.
Unit of work
A unit of work is a behavioral pattern in software development. Martin Fowler has defined it as everything one does during a business transaction which can affect the database. When the unit of work is finished, it will provide everything that needs to be done to change the database as a result of the work. A unit of work encapsulates one or more code repositories[de] and a list of actions to be performed which are necessary for the successful implementation of self-contained and consistent data change. A unit of work is also responsible for handling concurrency issues, and can be used for transactions and stability patterns.[de]
Copyright
A copyright is a type of intellectual property that gives its owner the exclusive legal right to copy, distribute, adapt, display, and perform a creative work, usually for a limited time. The creative work may be in a literary, artistic, educational, or musical form. Copyright is intended to protect the original expression of an idea in the form of a creative work, but not the idea itself. A copyright is subject to limitations based on public interest considerations, such as the fair use doctrine in the United States and fair dealing doctrine in the United Kingdom. Some jurisdictions require "fixing" copyrighted works in a tangible form. It is often shared among multiple authors, each of whom holds a set of rights to use or license the work, and who are commonly referred to as rights holders. These rights normally include reproduction, control over derivative works, distribution, public performance, and moral rights such as attribution. Copyrights can be granted by public law and are in that case considered "territorial rights". This means that copyrights granted by the law of a certain state do not extend beyond the territory of that specific jurisdiction. Copyrights of this type vary by country; many countries, and sometimes a large group of countries, have made agreements with other countries on procedures applicable when works "cross" national borders or national rights are inconsistent. Typically, the public law duration of a copyright expires 50 to 100 years after the creator dies, depending on the jurisdiction. Some countries require certain copyright formalities to establishing copyright, others recognize copyright in any completed work, without a formal registration. When the copyright of a work expires, it enters the public domain. == History == === Background === The concept of copyright developed after the printing press came into use in Europe in the 15th and 16th centuries. It was associated with a common law and rooted in the civil law system. The printing press made it much cheaper to produce works, but as there was initially no copyright law, anyone could buy or rent a press and print any text. Popular new works were immediately re-set and re-published by competitors, so printers needed a constant stream of new material. Fees paid to authors for new works were high and significantly supplemented the incomes of many academics. Printing brought profound social changes. The rise in literacy across Europe led to a dramatic increase in the demand for reading matter. Prices of reprints were low, so publications could be bought by poorer people, creating a mass audience. In German-language markets before the advent of copyright, technical materials, like academic papers and handbooks, were inexpensive and widely available; it has been suggested this contributed to Germany's industrial and economic success. === Conception === The concept of copyright first developed in England. In reaction to the printing of "scandalous books and pamphlets", the English Parliament passed the Licensing of the Press Act 1662, which required all intended publications to be registered with the government-approved Stationers' Company, giving the Stationers the right to regulate what material could be printed. The Statute of Anne, enacted in 1710 in England and Scotland, provided the first legislation to protect copyrights (but not authors' rights). The Copyright Act 1814 extended more rights for authors but did not protect British publications from being reprinted in the US. The Berne International Copyright Convention of 1886 finally provided protection for authors among the countries who signed the agreement, although the US did not join the Berne Convention until 1989. In the US, the Constitution grants Congress the right to establish copyright and patent laws. Shortly after the Constitution was passed, Congress enacted the Copyright Act of 1790, modeling it after the Statute of Anne. While the national law protected authors' published works, authority was granted to the states to protect authors' unpublished works. The most recent major overhaul of copyright in the US, the Copyright Act of 1976, extended federal copyright to works as soon as they are created and "fixed", without requiring publication or registration. State law continues to apply to unpublished works that are not otherwise copyrighted by federal law. This act also changed the calculation of copyright term from a fixed term (then a maximum of fifty-six years) to "life of the author plus 50 years". These changes brought the US closer to conformity with the Berne Convention, and in 1989 the United States further revised its copyright law and joined the Berne Convention officially. Copyright laws allow products of creative human activities, such as literary and artistic production, to be preferentially exploited and thus incentivized. Different cultural attitudes, social organizations, economic models and legal frameworks are seen to account for why copyright emerged in Europe and not, for example, in Asia. In the Middle Ages in Europe, there was generally a lack of any concept of literary property due to the general relations of production, the specific organization of literary production and the role of culture in society. The latter refers to the tendency of oral societies, such as that of Europe in the medieval period, to view knowledge as the product and expression of the collective, rather than to see it as individual property. However, with copyright laws, intellectual production comes to be seen as a product of an individual, with attendant rights. The most significant point is that patent and copyright laws support the expansion of the range of creative human activities that can be commodified. This parallels the ways in which capitalism led to the commodification of many aspects of social life that earlier had no monetary or economic value perse. Copyright has developed into a concept that has a significant effect on nearly every modern industry, including not just literary work, but also forms of creative work such as sound recordings, films, photographs, software, and architecture. === National copyrights === Often seen as the first real copyright law, the 1709 British Statute of Anne gave authors and the publishers to whom they did chose to license their works, the right to publish the author's creations for a fixed period, after which the copyright expired. It was "An Act for the Encouragement of Learning, by Vesting the Copies of Printed Books in the Authors or the Purchasers of such Copies, during the Times therein mentioned." The act also alluded to individual rights of the artist. It began: "Whereas Printers, Booksellers, and other Persons, have of late frequently taken the Liberty of Printing ... Books, and other Writings, without the Consent of the Authors ... to their very great Detriment, and too often to the Ruin of them and their Families:". A right to benefit financially from the work is articulated, and court rulings and legislation have recognized a right to control the work, such as ensuring that the integrity of it is preserved. An irrevocable right to be recognized as the work's creator appears in some countries' copyright laws. The Copyright Clause of the United States, Constitution (1787) authorized copyright legislation: "To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." That is, by guaranteeing them a period of time in which they alone could profit from their works, they would be enabled and encouraged to invest the time required to create them, and this would be good for society as a whole. A right to profit from the work has been the philosophical underpinning for much legislation extending the duration of copyright, to the life of the creator and beyond, to their heirs. Yet scholars like Lawrence Lessig have argued that copyright terms have been extended beyond the scope imagined by the Framers. Lessig refers to the Copyright Clause as the "Progress Clause" to emphasize the social dimension of intellectual property rights. The original length of copyright in the United States was 14 years, and it had to be explicitly applied for. If the author wished, they could apply for a second 14‑year monopoly grant, but after that the work entered the public domain, so it could be used and built upon by others. === Continental law === In many jurisdictions of the European continent, comparable legal concepts to copyright did exist from the 16th century on but did change under Napoleonic rule into another legal concept: authors' rights or creator's right laws, from French: droits d'auteur and German Urheberrecht. In many modern-day publications the terms copyright and authors' rights are being mixed, or used as translations, but in a juridical sense the legal concepts do essentially differ. Authors' rights are, generally speaking,
Content engineering
Content engineering is a term applied to an engineering specialty dealing with the complexities around the use of content in computer-facilitated environments. Content authoring and production, content management, content modeling, content conversion, and content use and repurposing are all areas involving this practice. It is not a specialty with wide industry recognition and is often performed on an ad hoc basis by members of software development or content production or marketing staff, but is beginning to be recognized as a necessary function in any complex content-centric project involving both content production as well as software system development mainly involving content management systems (CMS) or digital experience platforms (DXP). Content engineering tends to bridge the gap between groups involved in the production of content (publishing and editorial staff, marketing, sales, human resources) and more technologically oriented departments such as software development, or IT that put this content to use in web or other software-based environments, and requires an understanding of the issues and processes of both sides. Typically, content engineering involves extensive use of embedded XML technologies, XML being the most widespread language for representing structured content. Content management systems are a key technology often used in the practice of content engineering. == Definition == Content engineering is the practice of organizing the shape and structure of content by deploying content and metadata models, in authoring and publishing processes in a manner that meets the requirements of an organization's Content Strategy, and its implementation through the use of technology such as CMS, XML, schema markup, artificial intelligence, APIs and others. == Purpose and goal == In very general terms, content engineering practices aim to maximize the ROI of content through content reuse and improving efficiency of content marketing, content operations, content strategy. Content engineering can help address content challenges that fairly typical organizations face: Siloed content supply chains Duplicate content in a myriad of formats Inefficient content authoring workflows Chunky, unstructured content Outdated technology Technology in place does not match needs Inability to reuse content across channels (multi-channel content) Metadata and schema are not used Lack of standards for metadata Lack of findability of content for internal and external use Poor SEO performance Inability to implement personalization == Key skills == Content engineering draws on a combination of technical, strategic, and editorial competencies. Practitioners typically require proficiency across several domains: === Content modeling and information architecture === Content engineers design structured content models that define how content is created, stored, and distributed. This includes building taxonomies, ontologies, and metadata schemas that enable content reuse across channels and platforms. === Structured content and markup languages === Proficiency in XML, JSON, HTML, and schema.org markup is fundamental. Content engineers use these languages to structure content for machine readability, search engine optimization, and interoperability between systems. === Content management systems and platforms === Content engineers require working knowledge of content management systems (CMS), digital experience platforms (DXP), and headless CMS architectures. This includes configuring content types, workflows, and publishing pipelines within these systems. === Workflow design and automation === Designing and implementing content workflows - from authoring through review, approval, and distribution - is a core function. Increasingly, this involves configuring AI-assisted and agentic workflows that automate research, drafting, repurposing, and distribution tasks at scale. === Content strategy and editorial understanding === Unlike purely technical roles, content engineering requires a working understanding of content strategy, brand management, editorial standards, and audience analysis. Content engineers must translate strategic objectives into technical content structures and system configurations. === API integration and data interoperability === Content engineers work with APIs to connect content systems, analytics platforms, distribution channels, and third-party services. Understanding how content flows between systems is essential for enabling multi-channel publishing and content personalization. === Analytics and performance measurement === Measuring content effectiveness through web analytics, SEO performance data, and engagement metrics informs how content engineers refine structures, metadata, and distribution workflows. == The role of a content engineer == Content engineers bridge the divide between content strategists and producers and the developers and content managers who publish and distribute content. But rather than simply wedging themselves between these players, content engineers help define and facilitate the content structure during the entire content strategy, production and distribution cycle from beginning to end. As the role has evolved, content engineers are increasingly expected to build and manage AI-powered content systems, moving beyond traditional CMS configuration into agentic workflows that automate content research, production, and distribution. By integrating skills in business and technology, content engineers do not see content as static or finished. Rather, they look at the value of the content and how it can best be adapted and personalized to serve customers and emerging content platforms, technologies, and opportunities. === Create customer experience === Content marketing suffers from two fundamental limitations that constrain the true power and potential that a great content marketing plan can bring to a business' bottom line: Content relevance: how to make content more relevant and personalized to their audiences. The marketer and content strategist direct the customer experience itself, and the content engineer makes it happen with content structure, schema, metadata, microdata, taxonomy, and CMS topology. Content agility: Marketers who are burdened with one-size-fits-all content remain stuck managing their content rather than their customers' experience. Content engineers give marketers the "super powers" to move content-powered experiences across interfaces and personalization variants. === Break down barriers === Empower content strategists: Content engineers work with content strategists by helping them connect content not as a fixed message, but as a modular construct which can be channeled and manipulated. Enable content producers: A content engineer will work with a content producer by helping to find new sources of content and ways the content can be combined and presented. Guide and free developers: The content engineer helps translate marketing strategy into clear technical needs and functions developers can build into content management systems Enhance content management: Develop content structures that make it easier for content writers and content managers to author to a single, very usable, interface for even complex content types that might contain dozens of elements. Engineer content for success: Content engineers help all members of a marketing team work more smoothly, with the support and structures needed to get the most out of the content they produce. === Salary benchmarks === Content engineering roles command significantly higher salaries than traditional content marketing positions. In the United States, IC-level content engineers earn between $120,000 and $165,000 annually, while senior roles reach $160,000 to $220,000. Head of content engineering positions range from $200,000 to $280,000, and VP-level roles can exceed $375,000. The emergence of dedicated content engineer job postings from companies such as Exit Five reflects the growing recognition of the role as a distinct function within marketing organizations.
AS2
AS2 (Applicability Statement 2) is a specification on how to transport structured business-to-business data securely and reliably over the Internet. Security is achieved by using digital certificates and encryption. == Background == AS2 was created in 2002 by the IETF to replace AS1, which they created in the early 1990s. The adoption of AS2 grew rapidly throughout the early 2000s because major players in the retail and fast-moving consumer goods industries championed AS2. Walmart was the first major retailer to require its suppliers to use the AS2 protocol instead of relying on dial-up modems for ordering goods. Amazon, Target, Lowe's, Bed, Bath, & Beyond and thousands of others followed suit. Many other industries use the AS2 protocol, including healthcare, as AS2 meets legal HIPAA requirements. In some cases, AS2 is a way to bypass expensive value-added networks previously used for data interchange. == Technical overview == AS2 is specified in RFC 4130, and is based on HTTP and S/MIME. It was the second AS protocol developed and uses the same signing, encryption and MDN (as defined by RFC3798) conventions used in the original AS1 protocol introduced in the late 1990s by IETF. In other words: Files are encoded as "attachments" in a standardized S/MIME message (an AS2 message). AS2 does not specify the contents of the files. Usually, the file contents are in a standardized format that is separately agreed upon, such as XML or EDIFACT. AS2 messages are always sent using the HTTP or HTTPS protocol (Secure Sockets Layer — also known as SSL — is implied by HTTPS) and usually use the "POST" method (use of "GET" is rare). Messages can be signed, but do not have to be. Messages can be encrypted, but do not have to be. Messages may request a Message Disposition Notification (MDN) back if all went well, but do not have to request such a message. If the original AS2 message requested an MDN: Upon the receipt of the message and its successful decryption or signature validation (as necessary) a "success" MDN will be sent back to the original sender. This MDN is typically signed but never encrypted (unless temporarily encrypted in transit via HTTPS). Upon the receipt and successful verification of the signature on the MDN, the original sender will "know" that the recipient got their message (this provides the "Non-repudiation" element of AS2). If there are any problems receiving or interpreting the original AS2 message, a "failed" MDN may be sent back. However, part of the AS2 protocol states that the client must treat a lack of an MDN as a failure as well, so some AS2 receivers will not return an MDN in this case. Like any other AS file transfer, AS2 file transfers typically require both sides of the exchange to trade X.509 certificates and specific "trading partner" names before any transfers can take place. AS2 trading partner names can usually be any valid phrase. === MDN options === Unlike AS1 or AS3 file transfers, AS2 file transfers offer several "MDN return" options instead of the traditional options of "yes" or "no". Specifically, the choices are: ==== AS2 w/ "Sync" MDNs ==== Return Synchronous MDN via HTTP(S) ("AS2 Sync") - This popular option allows AS2 MDNs to be returned to AS2 message sender clients over the same HTTP connection they used to send the original message. This "MDN while you wait" capability makes "AS2 Sync" transfers the fastest of any type of AS file transfer, but it also keeps this flavor of MDN requests from being used with large files (which may time out in low-bandwidth situations). ==== AS2 w/ "ASync" MDNs ==== Return Asynchronous MDN via HTTP(S) (a.k.a. "AS2 Async") - This popular option allows AS2 MDNs to be returned to the AS2 message sender's server later over a different HTTP connection. This flavor of MDN request is usually used if large files are involved or if your trading partner's AS2 server has poor Internet service. ==== AS2 w/ "Email" MDNs ==== Return (Asynchronous) MDN via Email - This rarely used option allows AS2 MDNs to be returned to AS2 message senders via email rather than HTTP. Otherwise, it is similar to "AS2 Async (HTTP)". ==== AS2 w/ No MDNs ==== Do not return MDN - This option works like it does in any other AS protocol: the receiver of an AS2 message with this option set simply does not try to return an MDN to the AS2 message sender. ==== Filename preservation ==== AS2 filename preservation feature will be used to communicate the filename to the trading partner. The banking industry relies on filenames being communicated between trading partners. AS2 vendors are currently certifying that implementation of filename communication conforms to the standard and is interoperable. There are two profiles for filename preservation being optionally tested under AS2 testing: Filename preservation without MDN responses Filename preservation with an associated MDN response certification Walmart recommends contacting Drummond Group, LLC for more information on EDIINT AS2, or for a list of interoperable-testing AS2 software providers. == Benefits == For many businesses, the use of AS2 and electronic data interchange (EDI) is not a choice so much as it is a requirement of doing business with a large customer or partner. That said, AS2 is a universal protocol that has benefits, from both business and technology vantage points. === Business case === Cut costs by using the web for EDI file transfers, AS2 reduces the cost of transactions from expensive VANs. Extend EDI to more partners; with lower costs and universal web connectivity, AS2 allows organizations to implement EDI with partners worldwide that have little EDI infrastructure. Save time by eliminating the need to manually process orders. Eliminate errors by turning manual processes into automated processes. Universal solution — AS2 is established and tested, so no one has to re-invent the wheel. === Technological advantages === Leverage the web: if an organization can share data securely via the web, they already have much of the infrastructure for AS2. Unlimited EDI data — there are no practical limitations on transaction sizes via the web, and AS2 includes features for managing large transfers. Payload Agnostic — AS2 can be used to transport any type of document. While EDI X12, EDIFACT and XML are common, any mutually agreed-upon format may be transferred.
Kolmogorov–Arnold Networks
Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs), which rely on fixed activation functions and linear weights, KANs replace each weight with a learnable univariate function, often represented using splines. == History == KANs (Kolmogorov–Arnold Networks) were proposed by Liu et al. (2024) as a generalization of the Kolmogorov–Arnold representation theorem (KART), aiming to outperform MLPs in small-scale AI and scientific tasks. Before KANs, numerous studies explored KART's connections to neural networks or used it as a basis for designing new network architectures. In the 1980s and 1990s, early research applied KART to neural network design. Kůrková et al. (1992), Hecht-Nielsen (1987), and Nees (1994) established theoretical foundations for multilayer networks based on KART. Igelnik et al. (2003) introduced the Kolmogorov Spline Network using cubic splines to model complex functions. Sprecher (1996, 1997) introduced numerical methods for building network layers, while Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical neural network implementation. KART has also been used in other computational and theoretical fields. Coppejans (2004) developed nonparametric regression estimators using B-splines, Bryant (2008) applied it to high-dimensional image tasks, Liu (2015) investigated theoretical applications in optimal transport and image encryption, and more recently, Polar and Poluektov (2021) used Urysohn operators for efficient KART construction, while Fakhoury et al. (2022) introduced ExSpliNet, integrating KART with probabilistic trees and multivariate B-splines for improved function approximation. == Architecture == KANs are based on the Kolmogorov–Arnold representation theorem, which was linked to the 13th Hilbert problem. Given x = ( x 1 , x 2 , … , x n ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{n})} consisting of n variables, a multivariate continuous function f ( x ) {\displaystyle f(x)} can be represented as: f ( x ) = f ( x 1 , … , x n ) = ∑ q = 1 2 n + 1 Φ q ( ∑ p = 1 n φ q , p ( x p ) ) {\displaystyle f(x)=f(x_{1},\dots ,x_{n})=\sum _{q=1}^{2n+1}\Phi _{q}\left(\sum _{p=1}^{n}\varphi _{q,p}(x_{p})\right)} (1) This formulation contains two nested summations: an outer and an inner sum. The outer sum ∑ q = 1 2 n + 1 {\displaystyle \sum _{q=1}^{2n+1}} aggregates 2 n + 1 {\displaystyle 2n+1} terms, each involving a function Φ q : R → R {\displaystyle \Phi _{q}:\mathbb {R} \to \mathbb {R} } . The inner sum ∑ p = 1 n {\displaystyle \sum _{p=1}^{n}} computes n terms for each q, where each term φ q , p : [ 0 , 1 ] → R {\displaystyle \varphi _{q,p}:[0,1]\to \mathbb {R} } is a continuous function of the single variable x p {\displaystyle x_{p}} . The inner continuous functions φ q , p {\displaystyle \varphi _{q,p}} are universal, independent of f {\displaystyle f} , while the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds for all multivariate functions f {\displaystyle f} as proved in . If f {\displaystyle f} is continuous, then the outer functions Φ q {\displaystyle \Phi _{q}} are continuous; if f {\displaystyle f} is discontinuous, then the corresponding Φ q {\displaystyle \Phi _{q}} are generally discontinuous, while the inner functions φ q , p {\displaystyle \varphi _{q,p}} remain the same universal functions. Liu et al. proposed the name KAN. A general KAN network consisting of L layers takes x to generate the output as: K A N ( x ) = ( Φ L − 1 ∘ Φ L − 2 ∘ ⋯ ∘ Φ 1 ∘ Φ 0 ) x {\displaystyle \mathrm {KAN} (x)=(\Phi ^{L-1}\circ \Phi ^{L-2}\circ \cdots \circ \Phi ^{1}\circ \Phi ^{0})x} (3) Here, Φ l {\displaystyle \Phi ^{l}} is the function matrix of the l-th KAN layer or a set of pre-activations. Let i denote the neuron of the l-th layer and j the neuron of the (l+1)-th layer. The activation function φ j , i l {\displaystyle \varphi _{j,i}^{l}} connects (l, i) to (l+1, j): φ j , i l , l = 0 , … , L − 1 , i = 1 , … , n l , j = 1 , … , n l + 1 {\displaystyle \varphi _{j,i}^{l},\quad l=0,\dots ,L-1,\;i=1,\dots ,n_{l},\;j=1,\dots ,n_{l+1}} (4) where nl is the number of nodes of the l-th layer. Thus, the function matrix Φ l {\displaystyle \Phi ^{l}} can be represented as an n l + 1 × n l {\displaystyle n_{l+1}\times n_{l}} matrix of activations: x l + 1 = ( φ 1 , 1 l ( ⋅ ) φ 1 , 2 l ( ⋅ ) ⋯ φ 1 , n l l ( ⋅ ) φ 2 , 1 l ( ⋅ ) φ 2 , 2 l ( ⋅ ) ⋯ φ 2 , n l l ( ⋅ ) ⋮ ⋮ ⋱ ⋮ φ n l + 1 , 1 l ( ⋅ ) φ n l + 1 , 2 l ( ⋅ ) ⋯ φ n l + 1 , n l l ( ⋅ ) ) x l {\displaystyle x^{l+1}={\begin{pmatrix}\varphi _{1,1}^{l}(\cdot )&\varphi _{1,2}^{l}(\cdot )&\cdots &\varphi _{1,n_{l}}^{l}(\cdot )\\\varphi _{2,1}^{l}(\cdot )&\varphi _{2,2}^{l}(\cdot )&\cdots &\varphi _{2,n_{l}}^{l}(\cdot )\\\vdots &\vdots &\ddots &\vdots \\\varphi _{n_{l+1},1}^{l}(\cdot )&\varphi _{n_{l+1},2}^{l}(\cdot )&\cdots &\varphi _{n_{l+1},n_{l}}^{l}(\cdot )\end{pmatrix}}x^{l}} == Implementations == To make the KAN layers optimizable, the inner function is formed by the combination of spline and basic functions as the formula: φ ( x ) = w b b ( x ) + w s spline ( x ) {\displaystyle \varphi (x)=w_{b}\,b(x)+w_{s}\,{\text{spline}}(x)} where b ( x ) {\displaystyle b(x)} is the basic function, usually defined as s i l u ( x ) = x / ( 1 + e x ) {\displaystyle silu(x)=x/(1+e^{x})} and w b {\displaystyle w_{b}} is the base weight matrix. Also, w s {\displaystyle w_{s}} is the spline weight matrix and spline ( x ) {\displaystyle {\text{spline}}(x)} is the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)} Many studies suggested to use other polynomial and curve functions instead of B-spline to create new KAN variants. == Functions used == The choice of functional basis strongly influences the performance of KANs. Common function families include: B-splines: Provide locality, smoothness, and interpretability; they are the most widely used in current implementations. RBFs (include Gaussian RBFs): Capture localized features in data and are effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the maximum norm, making them useful for stable function representation. Rational function: Useful for approximating functions with singularities or sharp variations, as they can model asymptotic behavior better than polynomials. Fourier series: Capture periodic patterns effectively and are particularly useful in domains such as physics-informed machine learning. Wavelet functions (DoG, Mexican hat, Morlet, and Shannon): Used for feature extraction as they can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions in KANs. == Usage == In some modern neural architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and Transformers, KANs are typically used as drop-in substitutes for MLP layers. Despite KANs' general-purpose design, researchers have created and used them for a number of tasks: Scientific machine learning (SciML): Function fitting, partial differential equations (PDEs) and physical/mathematical laws. Continual learning: KANs better preserve previously learned information during incremental updates, avoiding catastrophic forgetting due to the locality of spline adjustments. Graph neural networks: Extensions such as Kolmogorov–Arnold Graph Neural Networks (KA-GNNs) integrate KAN modules into message-passing architectures, showing improvements in molecular property prediction tasks. Sensor data processing: Kolmogorov–Arnold Networks (KANs) have recently been applied to sensor data processing due to their ability to model complex nonlinear relationships with relatively few parameters and improved interpretability compared to conventional multilayer perceptrons. Applications include industrial soft sensors, biomedical signal analysis, remote sensing, and environmental monitoring systems. == Drawbacks == KANs can be computationally intensive and require a large number of parameters due to their use of polynomial functions to capture data.
Menu hack
A menu hack is a non-standard method of ordering food, usually at fast-food or fast casual restaurants, that offers a different result than what is explicitly stated on a menu. Menu hacks may range from a simple alternate flavor to "gaming the system" in order to obtain more food than normal. They are often spread on social media platforms such as TikTok, and are more popular with Generation Z, which has been known to customize their orders more than previous generations. Hacks are sometimes officially added to the menu after their popularity grows. However, in some cases, they have been criticized for overburdening fast food employees with outlandish requests, sparking debate as to whether certain menu hacks are unethical. The list of all possible menu hacks is called a secret menu. == History == The term "menu hack" stems from hacker culture and its tradition of overcoming previously imposed limitations. However, the tradition of ordering from a secret menu dates back to the early days of fast food. "Animal style" fries, a word of mouth menu item ordered from In-N-Out since the 1960s, was rumored to have been created by local surfers. In the Information Age, the rise of social media gave influencers the ability to communicate unique food combinations to their followers, which proved to go viral easily. Design mistakes in food ordering apps also proved to be easily exploitable. In some cases, these hacks boosted the profile of brands on social media, while in others, they caused financial harm when the company was unprepared to handle the sudden influx of unusual orders. One restaurant chain notable for the phenomenon is Chipotle Mexican Grill. A viral hack from Alexis Frost, suggesting a quesadilla with fajita vegetables inside, dipped in Chipotle vinaigrette mixed with sour cream, obtained 1.9 million views on TikTok, overloading the chain's workers, who had to work harder to prepare more vegetables and vinaigrette. Some restaurants began to deny the dish to customers, forcing them to only order meat and cheese on quesadillas. The company ultimately left the dish on the menu, but urged customers to stop ordering it via social media. When it later officially added the Fajita Quesadilla to the menu, digital sales nearly doubled. A method to order nachos, which are not officially on the menu, was also noted by customers. Starbucks is also famous for menu hacks, including the Pink Drink, a "Barbiecore" beverage in which coconut milk replaced the water in the strawberry açaí refresher. After it went viral, the company made it a permanent menu item and distributed it bottled in grocery stores. == Controversy == Menu hacks have been subject to a growing backlash, with employees stating that they "dread" younger customers due to the proliferation of unusual orders. Service industry workers, already overworked and underpaid, have called the rise of menu hacks and their difficulty to make an additional reason to unionize and demand higher wages.